1, 4, 9, 16, 25…

I eventually put the pattern up and asked if any square multiplied by 4 is always a square. They said yes and talked about the shape a dot representation of the number would make when multiplied by 4.

Then a student asked “Is a perfect square multiplied by a perfect square also always a perfect square?”

Well (a²)(b²) = (ab)²

We had a great 5 minute discussion about this, I had never thought of the product of two perfect squares, it is always fun when I learn along with them. I don’t talk enough about number theory, this was a great exercise in developing both number theory and sense.